The most probable single-molecule conductance of each member of a series of 12 conjugated molecular wires, 6 of which contain either a ruthenium or platinum center centrally placed within the backbone, has been determined. The measurement of a small, positive Seebeck coefficient has established that transmission through these molecules takes place by tunneling through the tail of the HOMO resonance near the middle of the HOMO-LUMO gap in each case. Despite the general similarities in the molecular lengths and frontier-orbital compositions, experimental and computationally determined trends in molecular conductance values across this series cannot be satisfactorily explained in terms of commonly discussed "single-parameter" models of junction conductance. Rather, the trends in molecular conductance are better rationalized from consideration of the complete molecular junction, with conductance values well described by transport calculations carried out at the DFT level of theory, on the basis of the Landauer-Büttiker model.